Infinite dimensional Riemannian symmetric spaces with fixed-sign curvature operator

Bruno Duchesne (1)

1 Einstein Institute of Mathematics

We associate to any Riemannian symmetric space (of finite or infinite dimension) a L∗-algebra, under the assumption that the curvature operator has a fixed sign. L∗- algebras are Lie algebras with a pleasant Hilbert space structure. The L∗-algebra that we construct, is a complete local isomorphism invariant and allows us to classify Riemannian symmetric spaces with fixed-sign curvature operator. The case of nonpositive curvature is emphasized

Mots clés: Riemannian symmetric spaces; L*-algebras

Domaines: Géométrie différentielle [math.DG]

Bruno Duchesne. Infinite dimensional Riemannian symmetric spaces with fixed-sign curvature operator. 2012. ⟨hal-00680969v2⟩